Week7 VJ - Trigonometry - Pythagorean Identities

University:
Victor Valley College
Course:
MATH 104 | Trigonometry
Academic year:

2024
Views:

111

Pages:

4
Author:

Kaylee Wiswell

This is the week7 Math104 YouTube Video Journal Assignment Kaylee Wiswell Name_______________________________ Watch Week7 (video7a) – Trigonometry - Pythagorean identities - - -- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 1) Label the Right Triangle with sides a, b, c and then give the Pythagorean Theorem. 2) Apply the Pythagorean Theorem to the unit circle below. (Show the same labeling done in the video) Recall, that the point P on the unit circle has an (x, y) point labeled 3) Switch the terms to show another form of the identity. Watch Week7 (video7b) – Trigonometry - Pythagorean identities - - -- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 1) What is the most important equation in Trigonometry? 2) What are the other two Pythagorean Identities? 3) What are the other two variations based on the first one? Watch Week7 (video7c) – Trigonometry - Pythagorean identities - - -- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 1) Label the Right triangle with sides a, b, c, and label angle x (follow the video) 2) Fill in the following from the video. 3) Show all of the work shown in the video to complete the following. Watch Week7 (video7d) – Trigonometry – Even/Odd identities - - -- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 1) Write down the even/odd identities Sin(- ϴ) = Csc(- ϴ) = Cos(- ϴ) = Sec(- ϴ) = Tan(- ϴ) = Cot(- ϴ) = 𝜋 𝜋 2) Use the graph of sine to show sin(− 2 ) = - sin( 2 ) 3) Use the graph of cosine to show cos(−𝜋) = - cos(𝜋) 4) Find the exact values of each (Use the odd/even identities and then the special right triangles) Show work from video. Sin( - 30°) = Cos( - 45°) = Sec( - 60°) = Tan( - 45°) = Watch Week7 (video7e) – Trigonometry – Even/Odd identities - - -- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 2 1) Given that cos(𝛳) = 3 Find cos( - ϴ) 2) Given that sin(ϴ) = 0.902 Find - sin( - ϴ) 1 3) Given that tan(−𝛳) = 3 4) Simplify: Find tan(ϴ) [Show all work from video] sec( - ϴ) + 3secϴ + 2sinϴ sin( - ϴ) Watch Week7 (video7f) – Trigonometry – Simplify Trig Expressions - - -- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 1) Write down the seven identities in the video that only involve Sine and Cosine. 2) Simplify: 3) Simplify: [Show all steps in video] csc(ϴ)·sin(ϴ) 4) Use sine and cosine identities (above) to Simplify the following. [Show all of the steps in the video] 5) Simplify: [Show all of the steps in the video] ( Sec(ϴ) + Csc(ϴ) )( Cos(ϴ) Sin(ϴ) )